Throughput Scaling Laws of Cognitive Radio Networks with Directional Transmission

Throughput scaling laws for two coexisting ad hoc networks with m primary users (PUs) and n secondary users (SUs) randomly distributed in an unit area has been widely studied. Early work showed that the secondary network performs as well as stand-alone networks, namely, the per-node throughput of the secondary networks is circle minus(1/root n log n). In this paper, we show that by exploiting directional spectrum opportunities in secondary networks, the SU throughput can be improved. If the main lobe of the SU antenna pattern can be as narrow as possible, then the SUs can achieve a per-node throughput of circle minus(root log n/n), which is circle minus(log n) times higher than the the throughput without directional transmission. If we consider practical constraints and assume the minimum angle of the main lobe is delta th, then the SU throughput gain is 2 pi/delta th compared with the throughput without directional transmission. We also explore the statistics of directional spectrum holes in this paper.